WASHINGTON — After the shooting of Rep. Gabrielle Giffords of Arizona and others at a supermarket in Tucson in early 2011, the Justice Department drew up a detailed list of steps the government could take to expand the background-check system in order to reduce the risk of guns falling into the hands of mentally ill people and criminals.

Most of the proposals, though, were shelved at the department a year ago as the election campaign heated up and as Congress conducted a politically charged investigation into the Operation Fast and Furious gun trafficking case, according to people familiar with the internal deliberations. It is not clear which, if any, of the conclusions were relayed to the White House.

It is far from clear whether any of the proposals — which centered on improving the background check system, and did not call for banning weapons — could have prevented the massacre at a Connecticut elementary school on Friday. But the recommendations could provide a blueprint if the Obama administration chooses to take more aggressive steps to curb gun violence.

President Barack Obama, in his weekly address on Saturday, said he wanted to take “meaningful action to prevent more tragedies like this; regardless of the politics.” He did not, however, give any details. The Justice Department’s list included several measures that, even if Congress did not act, Obama could enact by executive order.

It is far from certain, however, that the White House would be willing to wage a fight against the powerful gun-rights lobby or take attention from competing concerns, like negotiations over the looming fiscal deadline. While Obama’s words hinted at new steps to curb gun violence, Mayor Michael Bloomberg of New York and other gun-control advocates said they fell short of a concrete response.

Political pressure on the White House is building in some quarters of the Democratic Party. Rep. John Larson, D-Conn., for example, called for Congress to pass measures requiring background checks on all gun sales, as well as banning assault rifles and high-capacity clips.

“To do nothing in the face of pending disaster is to be complicit,” Larson said. “It’s time to act. It’s time to vote.”

Americans remain closely divided on the issue of gun rights, but public support for stricter gun-control laws has waned since 2008, according to several polls taken before the shootings in Newtown, Conn.

The Justice Department’s study, according to people familiar with the deliberations, did not focus on new restrictions on the kinds of weapons that most law-abiding Americans may purchase, on the premise that those would be nearly impossible to push through Congress.

Instead, it focused on ways to bolster the database the FBI uses for background checks on gun purchasers, including using information on file at other federal agencies. Certain people are barred from buying guns, including felons, drug users, those adjudicated mentally “defective,” illegal immigrants and people convicted of misdemeanor offenses related to domestic violence.

The study also proposed congressional action, including increasing grants to states as an incentive to voluntarily submit their own law enforcement information to the database — to about $100 million a year, up from about $11 million this year.